Find a two-digit number that is 5 times the sum of its digits.
Will the quotient or the remainder change if a divided number and the divisor are increased by 3 times?
Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.
Ten people wanted to found a club. To do this, they need to collect a certain amount of entrance fees. If the organizers were five people more, then each of them would have to pay £100 less. How much money did each one pay?
A cube with a side of 1 m was sawn into cubes with a side of 1 cm and they were in a row (along a straight line). How long was the line?
Burbot-Liman. Find the numbers that, when substituted for letters instead of the letters in the expression \(NALIM \times 4 = LIMAN\), fulfill the given equality (different letters correspond to different numbers, but identical letters correspond to identical numbers)
Seven nines written out in a series: 9 9 9 9 9 9 9. Put some “\(+\)” or “\(-\)” between some of them, so that the resultant expression equals 1989.
The tower clock chimes three times in 12 seconds. How long will six chimes last?
Are the sum and product odd or even for:
a) two even numbers?
b) two odd numbers?
c) an odd and an even number?
Determine all integer solutions of the equation \(yk = x^2 + x\). Where \(k\) is an integer greater than \(1\).